Multiple-band wave filter



swum v Sept 23 1924,

O. J. ZOBEL MULTIPLE BAND WAVE FILTER Filed April 30 lMllAAlll nnnvu I VEN TOR.

A TTORNEY or'ro .r. mnyormernnwoon, NEW JERSEY, .ASSIGNOR T AMERICAN TELEPHONE I a m TELEG HI GOMPANY, A CORPORATION OF NEW- YORK.

.r/iuL'rIrLE-BAnn wave FILTER.

- Application filed A ril 30, 1920. Serial at. 377,963.

To all whom it may concern: I Be-itknown that I, om J. ZOBEL, re-

sidin at Maplewood, in the county of Essex and tate of New Jersey, have invented cer- 5 tain Improvements in Multiple-Band Wave Filters, of which the followingis a specification.

This invention relates to selective circuits and more particularly to selectivecircuits of the type known as wave filters.

. In multiplex signaling, frequency selectivity has been heretofore obtained in cases where it has been desired to discriminate between different frequency hands by the employment of simplerecurrent networks comprising "arran' ements of inductances and ca 'acitiesk f these networks, thosewhich ave .been principally used are the so-called low pass, high pass and singleband filters described in the U. S.

patents to George A. Campbell, Nos. 1,227,-. 113 and 1,227 ,lldissued May 22,1917. These filters are characterized by the fact that currents lying within certain ranges of-frequencies are freely transmitted without sub stantial attenuation, while currents of other frequencies are very strongly attenuated. In general when a filterof this character is connected toa line whose impedance is tdpracticall a constant resistance, large impedence irregularities are introduced between the wave filter and the line, in the range of frequencies to be transmitted, since the characteristicimpedance of the filter at at any termination varies with frequency. These impedance irregularities at the frequenci'es to be transmitted are ob'ectionable, I not only from the standpoint 0 maximum --energy transferred from the line to the wave pester balance.

( One of the objects of this invention is to provide a wave filter-of the so-ca'lled constant is type, that is a filter so character- M ized that the product of the impedance of the series element of any section into the impedanceof the shunt element of that section will be proportional to the square of a constant and hence independent of fie-,

quency. Y 1 d Another object of the invention is to pro duce awave filter which will be in general 40 filter, but also from the standpeint of re:

,capable of transmitting over any preas-' signed number of frequency ranges. The filter of the present invention is quite ;dis-

tinct from that described in the Campbell patent, in this respect, since the Campbell filters were designed to transmit over a single range of frequencies or at most over two ranges of frequencies while attenuating all other frequencles.

Other and further objects of the invention will be more fully understood from the following detailed description when read in' connection with the accompanying drawing, Figures 1 and 2 of which illustrate curves characteristic of the filters of this invention, Fig. 3 of which is a simplified diagram of a recurrent network filter, while Figs. 4 to 9 inclusive are diagrams of elements which may be used in making up the filter of this invention.

The-wave filters forming the subject matter of this invention have a singly periodic structure consisting of a plurality of sections, as indicated in Fig. 3, each section comprising a series impedance element a, and a shunt impedancez These-impedance ele: 4 ments' are reactances, that is they are made up of inductances and capacities, in a manner morefully hereafter described. While '-tl1e discussion of these wave filters" is mari'ly on the basis that the elements are non-dissipative in characten'the inevitable introduction of dissipation will not matei rially alter the designs obtained. In order to minimize the transmission losses in the wave filter, there should be provided as large time constants for the inductances and ca-' pacities as is practicable in. each specific 'case.

.The computation for a filter on the assumed basis that its reactances are nondissipative is justified both by theoretical in- Vestigations and by practical tests. It is well known that the resistance of a-coil or a condenser can be made very small com-' pared to itsinductive 'reactance or capacity reactance and therefore the performance. of such a coil or condenser may be computed approximately with entire neglect of such slight resistance.

When the magnitude' of the inductances and 'capacities have been obtained on this basis and the type of coils and condensers giving these "magnitudes have been decided upon,the corresponding amounts of resistance necessarily introduced are then accurately taken account ofin practice when computing the current losses thru the wave- It is well known among engineers that at the sending end a long transmission line behaves the same as if its length were in- I finlte;

The characteristic impedance of a smooth line is its impedance at the sending end, assumin that the line is so long that it is, practical the same as if its ength were infinite. here is an analogous situae tion for filters of the type having recurrent sections. Their behavior is most easily computed in the first instance on the assumption that they extend with an infinite number of sections. from the sending end. In practice, a filter must have a finite number of sections and in that case it ma be terminated at the drop end by a suita 1e network to simulate the discarded infinite extension. The matter of providing such a network is not treated in the present specification.

It is well known that a smooth transmission line having uniform series impedance distributions 2, and uniform shunt impedance distributions 2,, per unit of length has the characteristic impedance I ale-72 I Such a line also has a propagation-constant:

pedance element 2 and a shunt impedance element 2 has a characteristic impedance at any termination which is a function of both the product and the ratio of'z and 2 and a .propa ation constant which is a func-' tion of t eir ratio, hence it is convenient to express both the characteristic impedance and propagation constant of the wave filter in terms of 7c and .y, the parameters of the corresponding smooth' line.

In order that the filter may be of the constant 1: type, it is necessary that the product of the series impedance 2, and the shunt impedance 2, per section should be a constant independent of frequency, that is By combining e nation 5 with equation 3, it is apparent t at the network transmits within a range of frequencies in which 2, lies between z =0 and z,r- ;|;i2k (6) There are two standpoints, transmission and attenuation, from which it' is possible to synthetically construct" any desired ,con-

Let .us first consider from the transstant in? wave filter. the construction of a filter mission requirements. a

From equation 6'it is apparent that a free transmission region occurs whenever the series element 2 becomes resonant, that is Assuming then that the desired wave filter should haven transmission regions, it is apparent that 2, must have n resonant points. These points may be obtained by constructing z, of n simple reactance components a a a all in parallel,

wherein each component takes care of one desiredresonant point of 2 As a specific example, take the case. of a filter which is desired to have three free transmission bands, one in the neighborhood of zero cycles, another in the neighborhood of infinity and still another at some intermediate frequency. For example, let one free trans- -mission band extend-from zero to frequency another free transmission band extend etween frequencies f and f, and a third free transmission band from frequency f, to infinity. The reactance curve for the element 2, at the various frequencies will be as indicated in Fig. 1. In this figure the reactance is zero at zero frequency and increases in a positive direction until it. becomes infinite at a point somewhere between frequency f and f When the reactance becomes infinite it suddenly changes sign and becomes negative and from this point the negative reactance? decreases until it becomes rero somewhere between I, and 7', for the- The reactance I second transmission band. now continues onthe upper slope in a positive direction, again becoming infinite between frequencies f and f again changing sign from positive to negative and then decreasing until it. again becomes zero' at mfimty.

The critical frequencies are determined" from equation 6, above, and-it will be seen that at the upper'critical frequency for the first transmission band 2 will be i2k. as

indicated in Fig. 1; at the lower critical frequency of the internal transmission band .2,

is 97270 at frequency. f at the higher critical frequency it becomes 11270 at frequency f,,;. and at the lower critical frequency of the infinite frequency transmission region the value of .2, becomes 2727s, at frequency f,,

- -The variation of transmission with frequency will nowbe as indicated in Fitz. 2,

which shows three bands of free transmission separated by two attenuation bands. A comparison of 2" with Fig.1 shows that the reactance becomes zero at some point in each transmissionband. Therefore, if we are to design the filter from the transmission requirements, it isappaI-entthat the series impedance element z may be constructed of three parallel elements, one of which includes a simple inductance L Such an element will have zero reactance at zero frequency. Another parallel element'may comprise a simple resonant circuit consisting of inducti being resonant at 'a frequency between and f and the other between f and f Such ance L and capacity O sinoe such an ele- 'ment may be made resonant at some desired frequency" between the frequencies f, and f Finally,- the third element may consist of a simple capacity, C which will have zero reactance at an infinite frequency.

The corresponding elements of the shunt impedance '2, may be readily determined from aconsideration of the fact that whereas the series element must be resonant at a given frequency for free transmission, the shunt element should be anti-resonant at the same frequency, in order that the least amount of current be diverted through. the shunt path. Consequently, theshunt impedance element a, shouldcontain a simple condenser G which will have an. infinite reactance at zero frequency. -An ant-i-res-.

onant' combination comprising inductance L and capacity'C should be providedfor a frequency between. the critical frequencies f, and f, of the internal transmission band.

Finally, a simple inductance L having an infinite reactance'at infinite frequency should be provided to correspond with the. capacity path C, of the series impedance element. Obviously, if additional internal transmissionbands are to be provided, such bands maybe accommodated by providing additional resonant circuits in parallel in the series element 2-, and corresponding antiresonant circuits in series in'the shunt impedance element 2 I A filter designed p'oducing the same results may be om a consideration of the at 'tenuation requirements only, although in' this case the physical form of the filter will be somewhat different. T Referring to Figs. 1

and 2' it is apparent that thelde'sign of a filter from attenuation requirements involves providing a series impedance element which shall have an infinite reactance atsome fre I1uency in each of the bands of attenuation.

n other words, at some point between freguency f and f the-'reactance should be innite and also at some point between fre-- uency f. and f,, the reactance should be in-.

nite. i The obvious construction to satisfy this requirement would be to construct the series element 2 of two anti-resonant elements in series, one anti-resonant element a design is illustrated in Fig, Obviously from an attenuation standpoint the corresponding requirement of the shunt element is that its-react-ance be zerov for the frequencies at which the series element-is resonant. The shunt element 2, should therefore'be constructed of two'resonant circuits in par allel, one circuit being resonant at afrequency between f and f and the other being resonant at a frequency between 7 and f While the filter of-Fig. 5 is apparently somewhat different in construction from that of Fig. 4, it will function in a manner which is identical therewith, if dissipation be dis, regarded, though byappropriate design dissipation may be present and make the filters of Figures 5 and 4 function identically. The equivalence of the two circuits will be more one path between point a and 6, containing a pure inductance L Such'a path is provided in Fig. 5 through the; two inductance readily apparent when it is considered that in Fig. 4 the-requirement. was to provide elements of the anti-resonant sets taken in for instance, from b to 0, one path extends through a capacity C and inductance L and L Obviously in Fig- 5 there is a path including inductance and capacity between 6 and c. In a similar manner in Fig. 4 there is a path including capacity C capacity G and inductance L An equivalent path including both inductance and capac'ity also occursin Fig. 5.

Still additional variations may be made in the design of either the series or the shunt impedance element. For instance, theseries impedance element may be constructed of asimple inductance in parallel with a circuit including a simple. capacity inseries with an anti-resonant set, as indicated in Fig. 6. This arrangement provides three ductance and capacity in series. Still an-,

other modification may be provided, as inpaths, one through a simple inductance, one through capacity'only, a third. through indicated in Fig. 7, by arranging a simple capacity element in parallel with a circuit including an inductance seriallyrelated to an anti-resonant set. 'Thelower path including the simple condenser in Fig. 7, corresponds to the path includingthe condenser C of Fig. 4, while the; other two paths in Fig. 4 are replaced by an inductance in semes with an antl-resonant clrcult.

- 4 for which it was substituted. Likewise,

as indicated inFig. 9, the condenser C, may be retained in the shunt impedance element .2 and the combination L C and L replaced by a simple inductance in parallel with the tuned circuit. The basis of this substitution will be at once seen from a com- .parison of the upper half of Fi 7 with the elements L 'L and C of ig. 4.

As a matter of fact, any one of the series impedance elements illustrated in Figs. 4, 5, 6 and 7 may be used with any one of the shunt impedance elements of Figs. 4, 5, 8

and 9, consequently there are sixteen combinations possible where three transmission bands are present. If additional transmission bands are to be provided, with consequent additional resonant and anti-resonant circuits in the series and shunt impedance elements respectivel still further rearrangements of the e ements maybe made, so that a much larger number of combinations will be possible.

In order to illustrate the manner in which the various inductances and capacities making up the shunt and series elements of the filter may be determined, the equations will be givenfor determining the inductance and capacity elements of impedances z, and .2 of Fig. 4, it being understood that the inductances and capacities may be worked out for.

the other cases described above, in a simi-- lar manner.

ran

Referring to Fig. 4, theseries element Z -ff -J") if we put for convenience,

component of inductance L in series with.

the capacity C and a capacitative component C The corresponding shunt element 2 is a series arran'gement'of a capacitative component G a simple anti-resonant component of inductance L in parallel with the capacity C and an inductive component L The constants of a, will first be determined and from these constants the values of the corresponding constants of 2 may then be obtained.

.In general, the value of k is put equal to the known resistance of the line in which the wave filter is to be placed. The critical frequencies separating the transmission and attenuation regions are also supposed to be known and will be designated as f f f and f (see Figs. 1 and 2) At these frequencies 2, must have the values i270, i2lc, i270 and 5270, respectively, as is apparent from consideration of equation 6.

The general expression for 2 in terms of frequency may be readily determined from the impedances of. each of the three parallel circuits, thus the impedance 2,, of the path including the inductance L may be expressed 11= 11Z where plis 21:

Similarly th nant path may be expressed and the impedance 2,, ing the capacity C 'will be From equations 7 ,-8 and 9 we may obtain 111 u n nP 10) u ia Lu u)? 3 12 :n w?

The relations also give e impedance 2,, of the reso of the path includexpressed by equations" 12,"?

by the or Lemma 7 such that Having obtained these values the inductances and'capaciti'es in z, are then found from the group of equations 13.

To derive the constants of the shunt element a from those of 2 we may proceed as follows: In a constant is type of filter.

as here designed, there is a re ation existmg between every component in 2 say 2 and its corresponding component 2 'm 2 Applying this relation toeach of the three components'of a we have er m agifl e 81%. M i; Q ggy; ym

(M fi 8) Equation 16 at once reduces to f k (19') 31 Similarly equation 18 reduces to za =k 20 C19 Equation 17 may be simplified and written From the form of eq'uation 21 it is apparent that if the equation is to be independent of the variable frequency, then L 0 must equal L 0 and must equal It. Through 1 v these relations we have at .once

. u 1: and hence. v

Equations 23 in conjunction with equations 13 give It will thus be seen that the design of the elements making up a constant In filter is'a fairly simple matter, although the al- .gebra becomes more complicated as the number of transmission bands is increased. It will also be observed that informulae 13 and 24 all the inductances are directly proportional to is and all the capacities are inversely pro ortioned to I0. I

If it' is esired to obtain the constants of some one of the other possible equivalent arrangements, such as those illustrated in Figs. '5 to 9 inclusive, the procedure is to obtain the impedance expression for 2 in terms of frequency, thereby obtaining an expression which is the same function of frequency as that expressed in equation 11.

Aset of relations similar to those set forth in equation 12' may then be obtained in terms of a, b, c and d and the new constants will then be suflicient to determine the inductances and capacities of the new design in terms of a, b, a and d. The constants of some other possible. equivalent impedance design for 2 may be similarly determined, for since 2 .2 equals 10 Equation 25 is the expression. for the value of the shunt impedance 2 in terms of v frequency and corresponds to equation 11 of the series impedance element.

It will be obvious'that the general principles herein disclosed may be embodied in many other organizations widely different from them illustrated, without departing I from the spirit of the invention as defined in the following claims.

In .this specification and in the following claims, reference is made to the frequency range, and in accordance with the well-recognized usage of mathematics, it will readily be understood that zero frequency is to be looked upon as a frequency of the whole range at one end thereof, and infinite frequency is to be looked upon as another'frequency at the other end of the range. By infinitefrequenc we mean a frequency so high that the p enomena are i not materially different from what they would be if it were made considerably higher. In other words, an infinite frequency is a frequency so high that the results obtained by making it high approach to limiting values.

What is claimed is:

1. A wave filter comprising a plurality of periodic sections, each section includin series impedance elements in parallel an shunt impedance elements in series so proportioned that the filter will have more than two bands of free transmission, the impedai ce of the filter being such that the product of the series impedance and the shunt impedance. of any section will be constant. 3

2. A wave filter coin rising a plurality of periodic sections, eac section includin series and shunt impedance elements, sai

series elements being arranged to provide a plurality of parallel paths, and all said elements being so proportioned that the filter will have more than two bands of free transmission.

3. A wave filter comprising a-p'luralit of periodic sections, each section mcluing series and shunt impedance elements constructed of ,inductances and ca acities, the inductances and capacities o the series elements being arranged to provide a-plurality of parallel fipaths of respectively vanishing reactance atkfiiifi'erent frequencies,

, and the. inductances and capacities of the series and shunt elements being so proportioned and related that the filter as a whole will have more than two bands of free transmission, the impedance ofthe filter being such that the product of the series impedance and the shunt impedence of any section will be a constant. a

4. A wave, filter comprising a plurality of periodic sections, each-section including series and shunt impedance elements constructed of inductances and capacities, the series elementsbein arranged to provide a plurality of paral el paths each of 'zero reactance at a respective frequency, the inductances and capacities of the series and shunt elements being so proportioned and related that the filter as a whole will have more than two bands of free transmission.

bands of transmission, said wave fi ter comprising a, number of'periodic sections, each 'section including "series and shunt impedance elements, said series impedance elements being constructed of capacit es and inductances so related that there Wlll be 9.,

within each of the bands of free transmission.

7 A wave filter having a plurality of free bands of transmission, said wave filter comprising a number of. periodic sections, each section including ser es .and shunt impedance elements, said shunt impedance elements being constructed of inductances and capacities so pro ortioned and related that a combination -0 infinite reactance will be path 'of'zero reactance at a frequency lying formed for a frequency lying within each band of free transmission.

8. The combination of a wave filter with apparatus having a substantially constant resistance for all frequencies of current, said "wave filter being of the constant 70 type with is equal to the resistance of said apparatus. f

9. The combination ofa long line of substantially constant resistance at- -all frelguencies, and a wave filter of the constant ype for which 70 is substantially equal to the said resistance of the line.

10. The combination of a wave filter and along line, whose impedance is substantially a constant" resistance at all frequencies, said filter having recurrent sections, each with series and shunt elements, the product of the impedances of such elements being constant and substantially equal to the 7 square of said resistance of the ine.

11. A wave filter comprising a plurality of periodic sections, each section including ser es and shunt impedance elements, the

series elements arranged to provide a plu-' rality of parallel paths, each of zero reactance at a certain frequency, and the shunt elements arranged in series, each being'of infinite reactance at the samefre uency as that for which a respective seriese ement is' resonant.

.12. A wave filter comprising a series coinponent impedance in paralleTand shunt component eing constant for var ing frequency.

5 13. A 'wave filter comprising a plurality of periodic sections, each section including a series impedance of zero reactance at two or more frequencies at-least one of those fre-' quencies being finite, and a shunt im edance 10 of infinite reactance at these same equen- Z 1,309;184 p W cies and so pro ortioned that the product of the series an shunt impedances will be i a constant, said wave-filter having two or more separate ranges of free transmission and two or more separate ranges of attenuation.

In testimony whereof, I, have signed name to this specification this 28th dayof April 1920.

. i OTTO J. ZOBEL. 

